In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Back ground: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, so the aim of the study was to evaluate its effect as a separating medium on some physical properties such as (surface roughness, water sorption and solubility) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separat

This study uses load factor and loss factor to determine the power losses of the electrical feeders. An approach is presented to calculate the power losses in the distribution system. The feeder’s technical data and daily operation recorded data are used to calculate and analyze power losses.

This paper presents more realistic method for calculating the power losses based on load and loss factors instead of the traditional methods of calculating the power losses that uses the RMS value of the load current which not consider the load varying with respect to the time. Eight 11kV feeders are taken as a case study for our work to calculate load factor, loss factor and power losses. Four of them (F40, F42, F43 and F

  This study  focused on a fundamental issue which was represented by ability of Iraqi central bank in facing the difficulty of determining  the optimal ratio of liquidity in the Iraqi banks in terms of the balancing between its obligations to the depositors and borrowers, and liquidate their funds on one hand and the risks on the other hand.the search aimed  for achieving the goals which represented by identifying the possibility of Iraqi banks to apply the regulations rules and  instructions  issued by central bank  of  Iraq in determining  ratio  of  liquidity and  its  appropriate with Iraqi  banks  action to implement  a  reasonable  profit to&

Objective: To determine the ability of uVDBP to discern SRNS from steroid-sensitive nephrotic syndrome (SSNS) in Iraqi children. Materials and Methods: This cross-sectional study enrolled children with SRNS (n=31) and SSNS (n=32) from the pediatric nephrology clinic of Babylon Hospital for Maternity and Pediatrics over three months. Patients' characteristics in terms of demographics, clinical data, and urinary investigations were collected. Quantitative analysis of uVDBP levels was undertaken via a commercially available ELISA kit. Results: The median uVDBP values were significantly higher (p-value<0.001) in the SRNS group (median=10.26, IQR=5.91 μg/mL) than in the SSNS group (median=0.953, IQR=4.12 μg/mL). A negative correlati

   Effect of antioxidants (vitamins C and E) (500mg/kg) was studied on function of testes in albino mice treated with hexavalent chromium (1000ppm). The results showed that exposure to hexavalent chromium caused a significant decrease in body weights, without changes in weight of testes, seminal vesicles and prostate. A significant decrease was observed in the percentage of dead sperms, sperms abnormalities, diameter of seminiferous tubules and the number of leydig cells. Degenerative changes and necrosis were observed in the lumen of seminiferous tubules. Treatment of hexavalent chromium-exposed mice with vitamin C caused improvement in weights and characters of sperms and improvement of the tissue of seminiferous tubules. Tre